Dance With Symbols or Crunch Numbers?

This was my last post of my Mathematics Plugged Blog. I will continue here, but concentrate more on the  methodology and technology aspects.

A numbers or a symbols person?

I really enjoy meeting Paul Wilmott from tie to time, and he once asked his readers in a blog post: are you a numbers or a symbols person? Expecting hard-sciemce people to be symbols and, say, accountants to be numbers people.

This is important for the maths education, but even within the mathematical disciplines it is not so clear.

IMO, it starts with the question: axiomatic or algorithmic mathematics? In axiomatic maths two functions are defined "identical" if they have the identical I/O relation. In algorithmic maths you need to take care of the economics (resources usage, performance, ..).

As a former algebraist I worked in axiomatic maths. But in my business life I combined.

Dance with symbols

In symbolic computation programs shall be able to manipulate symbols that can be mathematical expressions, geometrical objects, molecule structures … or even programs.

We describe problems in the language of mathematics and try to solve with symbolic computation  methods (exact, by closed form solutions). But the world of closed form solutions is usually a small world. Just think of the Black Scholes formula in quantitative finance (restricted to constant volatility).

It's all numbers

Many problems cannot be transformed into closed form solutions. You need numerical schemes (in most of the real world cases). You need them to solve models of material flows, chemical reactors, conservation of energy, financial risk management …

Good numerical schemes fit perfect along sub-domains where closed form solutions are available and do not lose accuracy or robustness "in between".

Asymptotic Maths

So, applied mathematics is symbols and numbers. Asymptotic maths is about the decomposition of a domain into sub-domains where exact solutions are available and their reintegration into one solution.

This is really critical. If you understand the power of the combination your complex systems will add values. You usually add value, if you do the most difficult work. It's valued and scarce because it is difficult.

Use the future technology

And luckily there is technology that leverages your problem solving power: Wolfram Technology.

At uni software plus we developed know-how packages and conducted projects for major players and innovators in various industry sectors from metallurgy to quant finance.

Uni software plus is a comparatively small outfit. But it is amazing, what complex systems we could and  can build - by knowledge-based programming, with built-in algorithms combining symbols and numbers.

You can too. We will be pleased to show you how.

How I Failed To Solve The Magic Forest Problem

I am more a bird than a frog. And this has consequences.

Here you find the episode that started with the goats, wolves and lions puzzle.

If you are interested how it has been solved, influenced by knowledge and skills, you should browse through the posts of the episode.

It recalls Marshall McLuhan's words: first we build the tools - then they build us. Learning arrangements affect the society in which they play a role not by the content delivered but by the learning arrangement itself.

Lessons learned

The mathematician, the physicist and the sw engineer used different approaches and tools. I, the abstractonaut, failed because I wanted too much in too short time.

However, the different approaches are driven by quality factors like understandability, generality, performance and elegance.

Knowledge based programming

This is of great relevance for complex systems - like quant finance systems. 

You need a rich language that enables programmers do build systems from bottom-up in a symbolic, declarative fashion and you need blazingly fast, accurate and robust algorithms that provide the operational semantics. 

Yes, discrete problems like the magic forrest can be solved elegantly without any mathematical shortcut. And, IMO, Sascha's functional magic forrest is a reference how far programming can go.

Knowledge based programming is about describing things in computational terms. 

The idea of symbolic languages is to describe things in the same way (pieces of data). The corresponding algorithmic knowledge base provides the engine that implements the symbolic language.

This is again a bird's view, but ...

A short story of being lucky

13 years ago, we made a fundamental decision, wrapping the methodical knowledge base for derivative and risk analytics, UnRisk engine, with the symbolic Mathematica language  - now Wolfram Language

From that date on, we built UnRisk in a bottom-up fashion. In UnRisk Financial Languages based on the UnRisk engines developed in co-evolution.

And our clients can do the same.

You Want To Quit Your Job To Start Your Own Business?

When you start your own business, it is just you and your ideas. Then you add customers and they shape you and that ideas - you find yourself in a co-evolution.

And it is on you to achieve a fit without freezing it.

In What I have Done Wrong I have pointed out that there are traps and how I tried to avoid them

But there are steps before and I try to point them out for innovation businesses:

Ask a few principle questions

In what business do you want to be in?
What technology, products, behavior, services ("product") will you be able to provide?
Who is your dream client?
Who will be your strongest competitor?
What differential advantages does your business provide for this client against this competitor?
Who is your dream partner?
Is your financing right?

Describe a few things in a compass

Targets and milestones
Brand promise
Core values

Outline a marketing strategy

Analyze and segment your markets
Select the segment where you can become leader because of your differential advantage in the competitive arena - describe as CATWOE
Actors (User)
Transformations (like knowledge into margins)
World View (your business principle)
Owner (you?)
Environment (who influences your business)
 Describe a rough marketing and promotion mix

Final questions before selling

Do you have identified the segment for leadership?
Are there known product deficiencies?
Are the prices right?
Is the timing right?
Do you know your position in the competitive arena well enough?
Do you have the right marketing resources?
Do you have stories for the right channels?
Are you prepared for insight sales?
Is your sales force fit?

Time to think about success factors?

Let me speak with the 14 keys of success Steve Jobs recommended and how I see them through the lens of UnRisk: Lessons of Steve Jobs


Don't believe in those who suggest you need to work your ass of - you need passion, to do things that matter for those who care.

Look into the numbers

Be patient, but look whether you can create enough cash flow to pay the costs of your business, the bills and food. It may be in a bootstrap arrangement, but you need to know the finical impact of your decisions. Don'r forget: you gave up a salary and you have to pay yourself.

Get help?

Coming from where you are to where you want to be?